This work presents a numerical approach for directly coupling this 0D LV-elastance boundary condition (or any simpler ODE-based boundary condition) to a 3D fluid-structure interaction LB solver. The methodology introduces (for both ODE-based as well as non-stationary boundaries) a discrete explicit-in-time extension to an LB non-equilibrium extrapolation method [1]}, [2]}, [3]} for fluid-only problems that has been previously proposed only for given (often analytical) Dirichlet-based pressure/velocity boundary conditions. The ultimate aim is to enable accurate physiological LV-aortic coupling conditions for cardiovascular studies of, for example, the effects of left ventricle contractility on pulsatile hemodynamics in the aorta. Section 2 presents the governing equations for the fluid, the solid and the LV-elastance models. Section 3 details the direct 0D-3D LV-coupling strategy that is introduced in this work, including a discussion of the loss of mathematical regularity of such a model from a discontinuity in the velocity upon valve closure (and the proposition of a smoothing operator in order to ensure a continuous transition). Section 4 provides algorithmic details of the complete solver, including the numerical methods employed for the solid as well as the fluid-structure interactions (both of which can be provided by any number of suitable schemes). Section 5 presents a variety of performance studies attesting to the valid implementation and the accuracy of the fluid and solid solvers presented in this paper. Finally, Section 6 considers a sample physiological study of oscillatory wall shear stress in a 3D aorta.
